Superfluid and Insulating Phases in an Interacting-Boson Model: Mean-Field Theory and the RPA

Sheshadri, Karthik; Krishnamurthy, H. R.; Pandit, Rahul; Ramakrishnan, T. V.

doi:10.1209/0295-5075/22/4/004

Cited by 438 publications

(547 citation statements)

References 16 publications

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“…Finally: minimize E g with respect to ψ for different values of κ, ω, and ∆ to obtain the phase diagram. At T = 0 this approach is operationally equivalent [17] to the Gutzwiller Ansatz (GA) variational wave function technique [39,40] often used, but can be extended to finite temperatures.…”

Section: Methodsmentioning

confidence: 99%

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Quantum phase transitions of light

et al. 2006

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Recently, condensed matter and atomic experiments have reached a length-scale and temperature regime where new quantum collective phenomena emerge. Finding such physics in systems of photons, however, is problematic, as photons typically do not interact with each other and can be created or destroyed at will. Here, we introduce a physical system of photons that exhibits strongly correlated dynamics on a meso-scale. By adding photons to a two-dimensional array of coupled optical cavities each containing a single two-level atom in the photon-blockade regime, we form dressed states, or polaritons, that are both long-lived and strongly interacting. Our zero temperature results predict that this photonic system will undergo a characteristic Mott insulator (excitations localised on each site) to superfluid (excitations delocalised across the lattice) quantum phase transition. Each cavity's impressive photon out-coupling potential may lead to actual devices based on these quantum manybody effects, as well as observable, tunable quantum simulators.The Jaynes-Cummings [1] model is arguably the most important model for understanding light-matter interactions. It describes the interaction of a single, quasiresonant optical cavity field with a two-level atom. The coupling between the atom and the photons leads to optical nonlinearities and an effective photon-photon repulsion. Perhaps the most extreme demonstration of this photonic repulsion is photon blockade, demonstrated recently by Birnbaum et al. [2], where photonic repulsion prevents more than one photon from being in the cavity at any one time. Photon blockade was initially theoretically described with a four-state system [3], with multiplication of the weak Kerr nonlinearity effected by placing a large number of atoms within each cavity. However, it was quickly realised that the photonic blockade mechanism does not persist in the limit of many atoms [4], rapidly degrading as the number of atoms per cavity is increased [5]. Later Rebic et al. showed that the nonlinear interaction afforded by placing a single two-level atom inside a cavity would suffice for realising photon blockade [6]. This observation was highly significant as it allowed the full weight of the Jaynes-Cummings model to be used to attack and understand this problem.To create an atom-photon system whose dynamics mirror those traditionally associated with strongly interacting condensed matter systems, we consider a twodimensional array of photonic bandgap cavities. Each cavity contains a single two-level atom, quasi-resonant with the cavity mode. Evanescent coupling between the cavities due to their proximity allows inter-cavity photon hopping. This configuration is depicted schematically in Fig. 1(a), where we have explicitly chosen three nearest neighbours per cavity (coordination number z = 3), for reasons explained below. Because we are considering small cavities, with volumes of order λ 3 where λ is the wavelength of the light, there will be strong atom-photon couplings that will dominate over the...

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Section: Methodsmentioning

confidence: 99%

“…To obtain the system's zero temperature properties, we use the procedure of Refs. [16,17] which is outlined in the Methods section. When ψ = 0 we have a Mott phase, characterised by a fixed number of excitations per site with no fluctuations, and ψ = 0 indicates a superfluid phase.…”

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confidence: 99%

Quantum phase transitions of light

et al. 2006

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“…Analytic studies using mean-field theory [6][7][8] and renormalization group techniques [6] led to a deeper physical understanding of the model. Strong coupling expansions [9,10] gave a better quantitative picture, while quantum Monte Carlo simulations [11][12][13][14][15] were carried out in one and two dimensions.…”

Section: Introductionmentioning

confidence: 99%

Bosons confined in optical lattices: The numerical renormalization group revisited

Pollet¹,

Rombouts²,

Heyde³

et al. 2004

Phys. Rev. A

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A Bose-Hubbard model, describing bosons in a harmonic trap with a superimposed optical lattice, is studied using a fast and accurate variational technique (MFϩNRG): the Gutzwiller mean-field (MF) ansatz is combined with a numerical renormalization group (NRG) procedure in order to improve on both. Results are presented for one, two, and three dimensions, with particular attention to the experimentally accessible momentum distribution and possible satellite peaks in this distribution. In one dimension, a comparison is made with exact results obtained using stochastic series expansion.

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“…As we will show below, a mass-density-wave (MDW) phase can also be obtained in an extended-Bose-Hubbard model. Mean-field theories [2][3][4]6 of such models yield the phases mentioned above and physically appealing pictures of the natures of these phases. However, especially in low dimensions, such mean-field theories cannot always uncover the types of correlations present in these phases or the natures of the transitions between these phases.…”

Section: Introductionmentioning

confidence: 98%

“…Progress in this field has been driven by an interplay between theory, 1-10 numerical simulations, [11][12][13][14] and experiments. The latter include studies of liquid 4 He in porous media like vycor or aerogel, 15 Bose-Einstein condensates trapped in optical lattices, 16,17 micro-fabricated Josephson-junction arrays, 18-20 the disorder-driven superconductor-insulator transition in thin films of superconducting materials like bismuth, 21 and flux lines in type-II superconductors pinned by columnar defects aligned with the external magnetic field. 22 Theoretical and numerical studies [2][3][4]7,11,12 have concentrated on the Bose-Hubbard model which exhibits superfluid (SF) and bosonicMott-insulator (MI) phases and, if onsite disorder is included, a Bose-glass (BG) phase too.…”

Section: Introductionmentioning

confidence: 99%

The one-dimensional extended Bose-Hubbard model

Pai

Pandit

2003

J Chem Sci

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Abstract.We use the finite-size, density-matrix-renormalization-group (DMRG) method to obtain the zero-temperature phase diagram of the one-dimensional, extended Bose-Hubbard model, for mean boson density ρ = 1, in the U-V plane (U and V are respectively, onsite and nearest-neighbour repulsive interactions between bosons). The phase diagram includes superfluid (SF), bosonic-Mott-insulator (MI), and mass-density-wave (MDW) phases. We determine the natures of the quantum phase transitions between these phases.Keywords. Boson systems; quantum statistical theory; ground state; elementary excitations; other topics in quantum fluids and solids; liquid and solid helium.

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Superfluid and Insulating Phases in an Interacting-Boson Model: Mean-Field Theory and the RPA

Cited by 438 publications

References 16 publications

Quantum phase transitions of light

Quantum phase transitions of light

Bosons confined in optical lattices: The numerical renormalization group revisited

The one-dimensional extended Bose-Hubbard model

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